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The block-localized wavefunction (BLW) approach is an ab initio valence bond (VB) method incorporating the efficiency of molecular orbital (MO) theory. It can generate the wavefunction for a resonance structure or diabatic state self-consistently by partitioning the overall electrons and primitive orbitals into several subgroups and expanding each...
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... we focus on individual hydrogen bonds in the four systems, the charge-transfer energy for each N-H‚‚‚OH 2 bond is -1.9, -2.2, -2.6, and -3.1 kcal/mol, in good correlation with the hydrogen bond distance R N-O ) 2.860, 2.840, 2.818, and 2.792 Å in the four optimal models. Similar to previous work, we also probed individual polarization contributions from the solute and solvent separately, and Table 4 lists the polarization energy of the solute by the solvent charge density in the absence of the solute, and the polarization energy of the solvent by the solute permanent (gas phase) charge density. Due to the coupling effect, the sum of individual polarization energies is slightly ...Context 2
... than the total polarization energy listed in Table 3. But Table 4 demonstrates that the solvent polarization effect is far more significant than the solute polarization effect. Figure 3-(c1) plots that the solvent polarization shifts the electron density from the O-H σ bond to the oxygen side, and this shifted electron density will be subsequently donated to the protons in ammonium ion as manifested by Figure 3 (c2). ...Citations
... For Ac 2 N 2 , we can also conduct block-localized wavefunction (BLW) computations at the PBE0 level, which is the simplest variant of VB theory and incorporates the efficiency of MO theory. [76][77][78][79] The computed delocalized energies at the PBE0 level are very close to those with the VBSCF method. The high delocalization energies for bonding orbitals are fully consistent with the AdNDP and QTAIM analysis, conrming the delocalization nature of two s and two p orbitals. ...
Understanding the bonding nature between actinides and main-group elements remains a key challenge in actinide chemistry due to the involvement of f orbitals. Herein, we propose a unique “aromaticity-assisted multiconfiguration” (AAM) model to elucidate the bonding nature in actinide nitrides (An2N2, An = Ac, Th, Pa, U). Each planar four-membered An2N2 with equivalent An–N bonds possesses four delocalized π electrons and four delocalized σ electrons, forming a new family of double Möbius aromaticity that contributes to the molecular stability. The unprecedented aromaticity further supports actinide nitrides to exhibit multiconfigurational characters, where the unpaired electrons (2, 4 or 6 in naked Th2N2, Pa2N2 or U2N2, respectively) either are spin-free and localized on metal centres or form metal–ligand bonds. High-level multiconfigurational computations confirm an open-shell singlet ground state for actinide nitrides, with small energy gaps to high spin states. This is consistent with the antiferromagnetic nature observed experimentally in uranium nitrides. The novel AAM bonding model can be authenticated in both experimentally identified compounds containing a U2N2 motif and other theoretically modelled An2N2 clusters and is thus expected to be a general chemical bonding pattern between actinides and main-group elements.
... Natural resonance theory (NRT), [26] and block-localized wavefunction analyses (BLW) [27] were also conducted to verify primary resonance mode of the cyclic-[Au(EH 2 )] 3 À anion fragments (2 a' and 2 b') and extra cyclic resonance energy (62.9 kcal/mol for 2 a' and 57.8 kcal/mol for 2 b'), which further confirmed the aromaticity within the cyclic-(AuE) 3 moiety and the relatively higher level of aromaticity in 2 a' ( Figure S22 and Figure S23). These results further prove that aromatic zwitterionic Lewis structures, cyclic-[Au(μ 2 -ER 2 )] 3 À [Au(PMe 3 )] + , are more stable than their nonpolarized Lewis structures. ...
Intramolecular π‐aromatization is a trait of many organic compounds that enhances the stability of their structures and polarizes related C−C π bonds. In contrast, rare study is focused on this phenomenon in metal clusters. Many existing homometallic clusters exhibit aromaticity, often characterized by nonpolar metal‐metal bonds and a high degree of symmetry. However, synthesizing low‐symmetric homometallic clusters with high‐polar metal‐metal bonds is challenging due to their limited thermodynamic stability. Herein, we report a facile strategy for the synthesis of [Au(μ2‐ER2)]3−AuPMe3 (E=Ge, Sn; R2=1,1,4,4‐tetrakis(trimethylsilyl)butane‐1,4‐diyl) clusters and reveal a novel stabilization mode, intramolecular σ‐aromatization. Our electronic structure analyses show that these low‐symmetric clusters possess a ten‐electron σ‐aromatic system, which is achieved via intramolecular σ‐aromatization. Moreover, the strength of σ‐aromaticity gives rise to a polarity‐tunable exo‐Au−Au bond.
... To assess the magnitude of aromatic stabilization in the tri-thorium ring, Lin and Mo used the simplified charged model cluster Th3 10+ derived from the Th3Cl6 4+ cage at its equilibrium geometry with the highest-occupied molecular orbital (HOMO) that visually resembles the corresponding 3c2e-type HOMO in the original (experimentally validated) model cluster by Boronski et al. [3] The authors used a sophisticated computational method called the block-localized wavefunction at the density functional theory (BLW-DFT) [12] to estimate aromatic stabilization in terms of the extra cyclic resonance energy (ECRE). The calculated ECRE value of 18.7 kcal mol -1 ( Figure S1, Supporting Information) falls between the corresponding values for the archetypical σ-aromatic H3 + (31.9 kcal mol -1 ) and non-aromatic Li3 + (0.2 kcal mol -1 ), which prompted Lin and Mo to make the conclusion that the tri-thorium ring is considerably σ-aromatic; for comparison, the aromatic stabilization energy in thiophene is about 18.6 kcal mol -1 . ...
... This is because strict separation of charge between the Th3Cl6 cage and the surrounding ligands in the model crystalline actinide cluster dramatically affects the ECRE in the Th3 core. Lin and Mo, [8] and Tomeček et al., [10] made the charged model cluster Th3Cl6 4+ by removing two K cations (the spectators) and three cyclooctatetraenyl dianion ligands (COT 2-) from the original neutral model by Boronski et al. [3] However, the covalent bond order [12] between each thorium atom and the corresponding COT ligand is equal to 0.96, which means almost perfect sharing of the 7s 2 electrons (Th) with the 8π-subsystem (COT) rather than transfer of two electrons to make the aromatic 10π-electron COT 2ligand. To illustrate to what extent separation of charge affects bonding in the core of the actinide cluster, we performed symmetry-constrained relativistic calculations of the 3c2e-orbital energy levels in Th3 10+ , Th3Cl6 4+ , Th3, and the original model by To the best of our knowledge, there is no reliable and universal method to quantitatively assess the effect of aromatic stabilization in all-metal clusters. ...
The recent discovery of the cyclically delocalized three-center two-electron σ-bonding in the crystalline actinide cluster isolated by Liddle and co-workers has sparked a heated debate on the role of molecular aromaticity on the periphery of the periodic table. It has been suggested that the tri-thorium ring at the heart of the cluster features considerable aromatic stabilization comparable to the heterocyclic π-aromatic rings such as thiophene. In this Communication we challenge previous conclusions by showing from first principles that the tri-thorium bonding does not fulfill the very fundamental requirement by IUPAC of being distinctly stabilized by cyclic delocalization of electrons, and therefore it should be classified as non-aromatic once and for all.
... The geometric and electronic structures of the studied imidazole derivatives IM and Me-IM were found by using density-functional theory (DFT) calculations to find the best bond lengths and bond angles [26][27][28][29]. The protonated species (first protonation) of these inhibitors, IMH + and Me-IMH + have alsobeen investigated to elucidate and compare their adsorption mechanisms on the aluminum surface. ...
The corrosion inhibiting effect of imidazole derivatives on aluminum was studied using density functional theory (DFT) calculations to assess the relationship between molecular structures and their corresponding efficiencies. The chemical reactivity of the neutral and protonated species (IM, Me-IM, IMH+ and Me-IMH+) was investigated, and the impact of methyl group substitution on the adsorption ability onto Al(111) surface was examined. Results revealed that the neutral species can be absorbed onto Al(111) surface by forming covalent bond N–Al, implying chemisorption as the mechanism of adsorption. It was also established that, the IMH+ and Me-IMH+ can be adsorbed via the Cl− anion, which was already firstly adsorbed onto the Al(111) surface. The DFT calculations align well with the experimental results, suggesting that introduction of a methyl group at the 2-position of the imidazole ring enhances the adsorption ability.
... The structural and electronic properties of model N-doped CNTs are obtained within the DFT approach with the help of the GAUSSIAN09 software. 34 The Kohn-Sham equations are solved employing the Perdew-Burke-Ernzerhof (PBE) expression for the exchange-correlation potential, [35][36][37] together with the 6-31g* basis set (including a single polarization function) proposed by Peterson et al. 38 which is a good compromise between computational costs and accuracy. We consider (5,5) single-and (4,4)@ (9,9) double-walled armchair open-ended nanotubes containing up to 312 atoms and with lengths as large as 19 Å, where the dangling bonds at the ends are tied off with hydrogen atoms. ...
We report a combined experimental and theoretical study dedicated to analyze the N 1s core-level binding energies (CLBE) in N-doped carbon nanotubes (N-CNTs). X-ray photoelectron spectroscopy (XPS) data is obtained...
... VB-DFT [65] is a nonempirical approach that partitions the system into two coupled subsets, one treated with the DFT scheme and the other by VB theory. The block-localized density functional theory (BLDFT) method proposed by Cembran et al. and Mo et al. [30,66] constructs the valence-bond-like diabatic states based on a block-localized wavefunction (BLW) method [67], which is an MO-based VB theory proposed by Mo et al., in which the localized MOs are used to retrace the VB concepts and properties with cheap computational costs. The BLDFT method is suitable for studying electron transfer reactions and representing reactive potential energy surfaces. ...
The accurate description of strongly correlated systems, also known as multireference systems, requires a balanced treatment of static and dynamic correlations and is an important target for developing quantum chemical methods. An appealing treatment to economically describe strongly correlated systems is the multireference density function theory (MRDFT) approach, in which the static correlation is included in the multiconfigurational wave function, while the density function includes the dynamic correlation. This mini-review focuses on the recent progress and applications of the density functional methods based on valence bond theory. A series of density functional valence bond (DFVB) methods are surveyed, including the dynamic correlation correction-based and Hamiltonian matrix correction-based DFVB methods, the hybrid one-parameter DFVB methods, the block-localized density functional theory and the multistate density functional theory. These methods have been applied to various chemical and physical property calculations of strongly correlated systems, including resonance energies, potential energy curves, spectroscopic constants, atomization energies, spin state energy gaps, excitation energies, and reaction barriers. Most of the test results show that the density functional methods based on VB theory give comparable accuracy but require lower computational cost than high-level quantum computational methods and thus provide a promising strategy for studying strongly correlated systems.
... Among them are van der Waals interactions (such as π-π stacking), hydrogen bonding, π-ion interactions, electrostatic interactions (including ion-ion, ion-dipole and dipole-dipole, also called ionic bonding), and interactions with varying degrees of covalency due to charge transfer [17][18][19][20][21]. This Essay discusses the valence bond (VB) perspectives of weak interactions, explaining briefly the theoretical background for VB theory [22][23][24][25], and its simplified variant namely the block diagonalized wavefunction (BLW) method [26][27][28]. For the sake of economy, we focus thereafter on two types of interactions: one is the so-called halogen bond, and the other is the weak dihydrogen interaction, e.g. ...
... In this Essay, we will describe the key points using this complementarity by employing ab initio VB theory and its simpler variant, the block-localized wavefunction (BLW) method [26][27][28], to analyze the halogen bond [53,64,108] and the CH···HC interactions in alkanes [75]. ...
Noncovalent interactions are ubiquitous and have been well recognized in chemistry, biology and material science. Yet, there are still recurring controversies over their natures, due to the wide range of noncovalent interaction terms. In this Essay, we employed the Valence Bond (VB) methods to address two types of interactions which recently have drawn intensive attention, i.e., the halogen bonding and the CH‧‧‧HC dihydrogen bonding. The VB methods have the advantage of interpreting molecular structures and properties in the term of electron-localized Lewis (resonance) states (structures), which thereby shed specific light on the alteration of the bonding patterns. Due to the electron localization nature of Lewis states, it is possible to define individually and measure both polarization and charge transfer effects which have different physical origins. We demonstrated that both the ab initio VB method and the block-localized wavefunction (BLW) method can provide consistent pictures for halogen bonding systems, where strong Lewis bases NH3, H2O and NMe3 partake as the halogen bond acceptors, and the halogen bond donors include dihalogen molecules and XNO2 (X = Cl, Br, I). Based on the structural, spectral, and energetic changes, we confirm the remarkable roles of charge transfer in these halogen bonding complexes. Although the weak C-H∙∙∙H-C interactions in alkane dimers and graphene sheets are thought to involve dispersion only, we show that this term embeds delicate yet important charge transfer, bond reorganization and polarization interactions.
... This type of analysis is referred to as energy decomposition analysis (EDA). Most EDA methods are based on the supermolecular approach, i.e., variational quantum chemical calculations are performed on both the molecular complex and its isolated fragments, and the interaction energy is decomposed by the use of intermediate wavefunctions [19][20][21][22][23][24][25][26][27]. There are also methods in which the interaction between the fragments is treated as a perturbation to the non-interacting system [5,22,28,29]. ...
A series of 26 hydrogen-bonded complexes between Br− and halogen, oxygen and sulfur hydrogen-bond (HB) donors is investigated at the M06-2X/6-311 + G(2df,2p) level of theory. Analysis using a model in which Br− is replaced by a point charge shows that the interaction energy (ΔE Int) of the complexes is accurately reproduced by the scaled interaction energy with the point charge (ΔE PC Int).This is demonstrated by ΔE Int = 0.86ΔE PC Int with a correlation coefficient, R^2 =0.999. The only outlier is (Br-H-Br)− , which generally is classified as a strong charge-transfer complex with covalent character rather than a HB complex. ΔE PC Int can be divided rigorously into an electrostatic contribution (ΔE PC ES) and a polarization contribution (ΔE PC Pol). Within the set of HB complexes investigated, the former varies between -7.2 and -32.7 kcal mol−1 , whereas the latter varies between -1.6 and -11.5 kcal mol−1. Compared to our previous study of halogen-bonded (XB) complexes between Br− and C-Br XB donors, the electrostatic contribution is generally stronger and the polarization contribution is generally weaker in the HB complexes. However, for both types of bonding, the variation in interaction strength can be reproduced accurately without invoking a charge-transfer term. For the Br− ···HF complex, the importance of charge penetration on the variation of the interaction energy with intermolecular distance is investigated. It is shown that the repulsive character of ΔE Int at short distances in this complex to a large extent can be attributed to charge penetration.
... In the past, DFT was used just for calculations of bond structure and properties of solids molecules; however, now DFT calculations are carried out for quantum chemical analysis. 14 The best methodology to devise DFT is given by Kohn and Sham in which they explained a practical approach for measuring the energy properties. The Thomas Fermi approximation which considers the energy and density relationship and its effects supports much of the DFT studies. ...
Imines are multipurpose pharmacophores, simply accessible compounds, and have a broad range of usage in several areas of chemistry especially in medicine. Two novel compound imines, (E)-4-methyl-2-((o-tolylimino)methyl)phenol (1) and (E)-2-(((4-methoxybenzyl)imino)methyl)-4-methylphenol (2), were synthesized with effective product via reported protocol in the literature. Single crystal X-ray diffraction (SCXRD) was employed for structural exposition, disclosing that both compounds are orthorhombic. To optimize the newly designed imines, a B3LYP functional with a basis set 6-31G(d,p) was mainly considered. DFT results were utilized to check correlation between the data recovered from SCXRD outcomes and also to measure the energy difference. Hirshfeld surface study was done to demonstrate the intermolecular contacts along the percentage of interaction in the overall crystalline compound. Molecular operating environment program was tested against AChE and BChE enzymes to perform a modeling study of the compounds. The docking score and binding affinity of the compounds revealed that 2 showed comparatively more inhibition than 1. In silico ADMET studies exposed the physiochemical nature of these novel compounds, and it also unveiled that both compounds behaved as drug-like candidates.
... Here we performed a density functional theory (DFT) study with our developed block-localized wave function (BLW) method where the electron transfer among interacting moieties can be strictly deactivated. 43,44 All regular DFT computations were performed using Gaussian 16 software 45 with the Minnesota density functional (M06-2X) 46−48 and the all-electron 6-311+ +G(d,p) basis set augmented with the Grimme D3 dispersion correction. 49 The BLW computations at the same M06-2X-D3/6-311++G(d,p) theoretical level, 43,44 however, were carried out with GAMESS 50 to which our BLW code was ported in our laboratories. ...
... 43,44 All regular DFT computations were performed using Gaussian 16 software 45 with the Minnesota density functional (M06-2X) 46−48 and the all-electron 6-311+ +G(d,p) basis set augmented with the Grimme D3 dispersion correction. 49 The BLW computations at the same M06-2X-D3/6-311++G(d,p) theoretical level, 43,44 however, were carried out with GAMESS 50 to which our BLW code was ported in our laboratories. The BLW method is a variant of ab initio valence bond (VB) theory 51−53 and can derive electron strictly localized states (i.e., Lewis states) self-consistently. ...
